As a filter used in a communication device such as a mobile phone, there has been known a ladder-type filter in which piezoelectric thin film resonators each including a lower electrode and an upper electrode sandwiching a piezoelectric substance are connected in a ladder form. A duplexer and a module including a plurality of filters may be installed in a communication device.
When large electrical power is input to a piezoelectric thin film resonator, non-linearity due to the c-axis orientation of a piezoelectric substance causes secondary distortion (second harmonic) in output signals. As a method of reducing the secondary distortion, it has been known to serially divide a piezoelectric thin film resonator constituting a ladder-type filter and make the electrode of one of the divided resonators in the c-axis orientation direction or the polarization axis direction of the piezoelectric substance have an identical electric potential to the electric potential of the electrode of the other of the divided resonators in the c-axis orientation direction or the polarization axis direction of the piezoelectric substance, or to divide a piezoelectric thin film resonator in parallel and make the electrode of one of the divided resonators in the c-axis orientation direction or the polarization axis direction of the piezoelectric substance have an electric potential opposite to the electric potential of the electrode of the other of the divided resonators in the c-axis orientation direction or the polarization axis direction of the piezoelectric substance as disclosed in, for example, Japanese Patent Application Publication No. 2008-85989 (Patent Document 1).
In the structure where a metal layer is located to cover a plurality of piezoelectric thin film resonators located on the substrate, the deterioration of the characteristics may be caused by a parasitic capacitance between the electrodes constituting the piezoelectric thin film resonator and the metal layer. To inhibit the deterioration of the characteristics, it has been known to connect an inductor in series between the metal layer and a ground as disclosed in, for example, Japanese Patent Application Publication No. 2008-508822. In a ladder-type filter using a piezoelectric thin film resonator, the deterioration of the filter characteristic may be caused by parasitic capacitance formed by opposing the lower electrode and the upper electrode in a region other than a cavity. To inhibit the deterioration of the filter characteristic, it has been known to extend the upper electrode from the resonator in only one direction in all series resonators as disclosed in, for example, Japanese Patent Application Publication No. 2008-141561.
With reference to Patent Document 1, it may be considered to divide a parallel resonator in series or in parallel to reduce secondary distortion in an acoustic wave filter including a series resonator connected in series and a parallel resonator connected in parallel between an input terminal and an output terminal. However, it has been newly found that secondary distortion locally increases when the parallel resonator is divided in series or in parallel.